Functions
More of Fxn
Transformation of Fxn
Fxn, distance, mid, circles
Modeling with Fxn
100
Find the domain and range: {(0, 9.1), (10, 6.7), (20, 10.7), (30, 13.2), (40, 21.2)}.
What is
Domain: {0, 10, 20, 30, 40}
Range: {9.1, 6.7, 10.7, 13.2, 21.2}
100
What are x-intercepts and y-intercepts of a graph?
What is x-intercepts are x-coordinates of a point where the graph intersects the x-axis and corresponding y-coordinate is always zero. What is y-intercepts are y-coordinates of a point where the graph intersects the y-axis and corresponding x-coordinate is always zero.
100
List three points that lie on the graph of the given function.
g(x) = x2 + 2
What is (0, 2), (1, 3), (-1, 3)
100
Find the domain of each function.
g(x) = square root of (x - 2) / (x - 5)
What is [2, 5) U (5, infinity)
100
In 2000, the average weekly salary for workers in the US was $567. This amount has increased by approximately $15 per year.
a. Express the average weekly salary for US workers, W, as a function of the number of years after 2000, x.
b. If this trend continues, in which year will the average weekly salary be $882?
What is
a. W(x) = 567 + 15x
b. 882 = 567 + 15x so 21 years after 2000 - 2021
200
What is a vertical line test? What does it do?
What is if any vertical line intersects a graph in more than one point, the graph does not define y as a function of x. If a function passes the vertical line test, it is a function.
200
The following coordinates are from a graph of a function. Determine if it's a function or not.
{(1, 3), (2, 4), (10, 4), (1, 9)}
What is it is not a function
200
List three points that lie on the graph of the given function.
g(x) = square root of (3 - x)
What is (3, 0), (2, 1), (-1, 2)
200
Find an equation for f-1(x), the inverse function.
f(x) = square root of x + 1
What is f-1(x) = (x - 1)2 , x > and equal to 1
200
The bus fare in a city is $1.25. People who use the bus have the option of purchasing a monthly discount pass for $21.00. With the discount pass, the fare is reduced to $0.50.
a. Express the total monthly cost to use the bus without a discount pass, f, as a function of the number of times in a month the bus is used, x.
b. Express the total monthly cost to use the bus with a discount pass, g, as a function of the number of times in a month the bus is used, x.
c. Determine the number of times in a month the bus must be used so that the total monthly cost without the discount pass is the same as the total monthly cost with the discount pass. What will be the monthly cost for each option?
What is
a. f(x) = 1.25x
b. g(x) = 21 + 0.5x
c. If a person crosses the bridge 28 times the cost will be $35 for both options
300
Determine whether the equation defines y as a function of x: 2x + y2 = 6
What is since more than one value of y can be obtained from some values of x, y is not a function of x
300
Determine whether the graph of each equation is symmetric with respect to the y-axis, x-axis, the origin, more than one of these, or none of these.
x2 + y2 = 17
What is the function is symmetric with respect to the y-axis, x-axis, and the origin
300
List three points that lie on the graph of the given function.
r(x) = 1/2 |x +2|
What is (-4, 1), (-2, 0), (2, 2)
300
Find the distance between the pair of points.
(-4, 3) and (-2, 5)
What is 2 * square root of 2
300
A football team plays in a large stadium. With a ticket price of $20, the average attendance at recent games has been 30,000. A market survey indicates that for each $1 increase in the ticket price, attendance decreases by 500.
a. express the number of spectators at a baseball game, N, as a function of the ticket price, x.
b. Express the revenue from a baseball game, R, as a function of the ticket price, x.
What is
a. N(x) = 30,000 - 500(x-20)
N(x) = 40,000 - 500x
b. R(x) = -500x2 + 40,000x
400
Determine whether the function is even, odd, or neither. State each function's symmetry.
F(x) = x4-2x2+1
What is function is even and symmetric with respect to y-axis
400
Write an equation in general form for the line passing through (-12, -1) and perpendicular to the line whose equation is 6x - y - 4 = 0
What is x + 6y + 18 = 0
400
List three points that lie on the graph of the given function.
g(x) = 1/2 (x - 1)2 + 1
What is (1, 1), (3, 3), (-1, 3)
400
Write the standard form of the equation of the circle with the given center and radius.
Center (-2, 4), r = 6
What is (x + 2)2 + (y - 4)2 = 36
400
Pp. 293 #31
What is A(x) = x2 + (40/x)
500
Identify the relative maxima and minima for the graph of f.
What is
f has a relative maximum at x = −1.
f has a relative minimum at x = 1.
500
Find (f o g)(x) and the domain of (f o g).
f(x) = x / (x+1), g(x) = 4/x
What is (f o g)(x) = 4/(4+x) and domain: (negative infinity, -4) U (-4, 0) U (0, infinity)
500
List three points that lie on the graph of the given function.
r(x) = -2 * cube root of (-x)
What is (0, 0), (1, 2), and (-1, -2)
500
Give the center and radius of the circle:
x2 + y2 - 4x + 2y - 4 = 0
What is center (2, -1) and radius of 3
500
pp. 294 #39
What is
a. A(x) = 2x*square root of 4 - x2
b.P(x) = 4x + 2*square root of 4 - x2